The privileged spectrum of cnoidal ion holes and its extension by imperfect ion trapping |
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Authors: | Hans Schamel Nilakshi Das Prathana Borah |
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Institution: | 1. Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany;2. Department of Physics, Tezpur University, Assam, 784028, India |
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Abstract: | The fundamental properties of nonlinear ion hole modes propagating in current-driven collisionless plasmas are derived. Making use of Schamel's alternative method their spatial structure and phase velocities are analyzed and found to depend crucially on the used trapped ion distribution . A regular represents a continuous spectrum, which is called privileged or perfect since it yields a definite and appears most realistic. A singular , on the other hand, involving jumps and moderate slope singularities at the separatrix, does reveal further classes of hole equilibria at the cost, however, of a well-defined . This explains why Bernstein, Greene, Kruskal (BGK)-solutions of the Vlasov–Poisson system, exhibiting a strong slope singularity of their derived trapped particle distribution, can principally not provide definite . The nonlinear dispersion relation (or ) of privileged ion holes, on the other hand, is equivalent with that of cnoidal electron holes, i.e. in addition to the ordinary ion acoustic branch there exists a correspondence to the “Langmuir” branch and to the multiple “slow electron acoustic” branches, reflecting different trapping scenarios. |
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Keywords: | Solitary and cnoidal ion holes BGK waves Schamel-like distribution functions Trapping nonlinearity Nonlinear dispersion relation Failure of linear Landau approach |
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